• Communications for Statistical Applications and Methods
• /
• 제30권3호
• /
• pp.227-244
• /
• 2023

In this paper, a depth-based nonparametric test for a multivariate two-sample scale problem is proposed. The proposed test statistic is based on the depth-induced ranks and is thus distribution-free. In this article, the depth values of data points of one sample are calculated with respect to the other sample or distribution and vice versa. A comprehensive simulation study is used to examine the performance of the proposed test for symmetric as well as skewed distributions. Comparison of the proposed test with the existing depth-based nonparametric tests is accomplished through empirical powers over different depth functions. The simulation study admits that the proposed test outperforms existing nonparametric depth-based tests for symmetric and skewed distributions. Finally, an actual life data set is used to demonstrate the applicability of the proposed test.

• 응용통계연구
• /
• 제28권3호
• /
• pp.573-581
• /
• 2015

이 논문에서는 일표본 위치검정에서 표본크기를 결정하는데 일반적으로 사용되고 있는 근사분포방법의 문제점에 대해 알아본다. 모의실험 결과 이들 근사분포방법은 검정력의 명목수준에 도달하지 않는 것으로 나타났으며 이에 대한 개선이 필요한 것으로 나타났다. 이 논문에서는 검정통계량의 정확분포를 이용한 표본크기 결정에 대해 알아보고 이를 통한 표본크기의 검정력이 명목수준을 충족하는 것을 보인다.

• Journal of the Korean Data and Information Science Society
• /
• 제15권3호
• /
• pp.523-529
• /
• 2004

In Korea, mathematics education has been changed according to the 7th national mathematics curriculum renovated by the Ministry of Education and Human Resources Development announcement in 1997. The education of probability and Statistics has been carried out as a part of this curriculum. We analyze and compare 3 kinds of mathematics textbooks for 10-12 grade students. Descriptions of random variable, sample variance and sample standard deviation, distribution of sample mean, and etc. which are on some textbooks, are misleaded in school education. We suggest the unbiased estimator of sample variance in textbooks and distributions of sample means with normal population assumption.

• 품질경영학회지
• /
• 제33권3호
• /
• pp.149-155
• /
• 2005

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• 한국품질경영학회:학술대회논문집
• /
• 한국품질경영학회 2006년도 춘계학술대회
• /
• pp.135-141
• /
• 2006

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• 한국전문물리치료학회지
• /
• 제23권2호
• /
• pp.93-99
• /
• 2016

Background: Parametric statistical procedures are typically conducted under the condition in which a sample distribution is statistically identical with its population. In reality, investigators use inferential statistics to estimate parameters based on the sample drawn because population distributions are unknown. The uncertainty of limited data from the sample such as lack of sample size may be a challenge in most rehabilitation studies. Objects: The purpose of this study is to review the bootstrapping method to overcome shortcomings of limited sample size in rehabilitation studies. Methods: Articles were reviewed. Results: Bootstrapping method is a statistical procedure that permits the iterative re-sampling with replacement from a sample when the population distribution is unknown. This statistical procedure is to enhance the representativeness of the population being studied and to determine estimates of the parameters when sample size are too limited to generalize the study outcome to target population. The bootstrapping method would overcome limitations such as type II error resulting from small sample sizes. An application on a typical data of a study represented how to deal with challenges of estimating a parameter from small sample size and enhance the uncertainty with optimal confidence intervals and levels. Conclusion: Bootstrapping method may be an effective statistical procedure reducing the standard error of population parameters under the condition requiring both acceptable confidence intervals and confidence level (i.e., p=.05).

• Journal of the Korean Statistical Society
• /
• 제17권2호
• /
• pp.61-80
• /
• 1988

For testing homogeneity of scale parameters aginst ordered alternatives, some nonparametric test statistics based on pairwise ranking method are proposed. The proposed tests are distribution-free. The asymptotic distributions of the proposed statistcs are also investigated. It is shown that the Pitman efficiencies of the proposed rank tests are the same as those of the corresponding two-sample rank tests in the scale problem. A small-sample Monte Carlo study is also performed. The results show that the proposed tests are robust and efficient.

• Journal of the Korean Statistical Society
• /
• 제27권4호
• /
• pp.397-405
• /
• 1998

We develop parametric bootstrap model selection criteria in an example to fit a random sample to either a general normal distribution or a normal distribution with prespecified mean. We apply the bootstrap methods in two ways; one considers the direct substitution of estimated parameter for the unknown parameter, and the other focuses on the bias correction. These bootstrap model selection criteria are compared with AIC. We illustrate that all the selection rules reduce to the one sample t-test, where the cutoff points converge to some certain points as the sample size increases.

• 소음진동
• /
• 제8권5호
• /
• pp.814-820
• /
• 1998

Vibration data from two blasting sites were analyzed to determine the sufficient sample number for blasting vibration estimation. Most important result is that much more than 30 sample data and succeeding measurement are necessary to estimate confident blasting vibration level and to determine limit scaled distance.

• Journal of the Korean Data and Information Science Society
• /
• 제1권
• /
• pp.59-65
• /
• 1990

The Edgeworth expansion, the Roy-Tiku method and the bootstrap method for approximating the distribution of the sample variance are compared through the Monte Carlo simulation study.